Numéro |
J. Phys. IV France
Volume 116, October 2004
|
|
---|---|---|
Page(s) | 89 - 132 | |
DOI | https://doi.org/10.1051/jp4:2004116004 |
J. Phys. IV France 116 (2004) 89-132
DOI: 10.1051/jp4:2004116004
Simple theoretical tools for low dimension Bose gases
Y. CastinLaboratoire Kastler Brossel, ENS, 24 rue Lhomond, 75 231 Paris, France
Abstract
We first consider an exactly solvable classical field model
to understand the coherence properties and the density
fluctuations of a one-dimensional (1D) weakly interacting
degenerate
Bose gas with repulsive interactions at temperatures
larger than the chemical potential.
In a second part, using a lattice model for the quantum field,
we explain how to carefully generalize the usual Bogoliubov
approach to study a degenerate and weakly interacting Bose gas
in 1D, 2D or 3D in the regime of weak density fluctuations.
In the last part, using the mapping to an ideal Fermi gas in second
quantized formalism,
we calculate and discuss physically the density fluctuations and the
coherence properties of a gas of impenetrable bosons in 1D.
© EDP Sciences 2004